Thermal Convection in Rotating Bi‐Disperse Porous Medium With Local Thermal Nonequilibrium

ABSTRACT We investigate a model that describes convection within a porous material, which has a structural framework with large pores and additional small cracks or fissures, when the fluid undergoes rotation about the axis perpendicular to the layer and complies with gravity. The model applies the Brinkman theory within the macro‐pores and the Darcy theory in the micro‐pores, representing thermal convection in a dual‐porosity medium. The theory also includes local thermal nonequilibrium (LTNE), which means there can be different temperatures between the solid parts and the fluid in both the large and small pores. We conducted linear and nonlinear stability analyses to determine the effect of the problem parameters on the system's stability. Our findings reveal that the onset of linear instability aligns with the threshold for nonlinear stability, suggesting that the linear theory effectively captures the dynamics of the onset of thermal convection. The results of the current study confirmed the stabilizing effect of the heat transfer parameter, thermal conductivity ratio, ratio of macro‐pore to micro‐pore porosity, Brinkman coefficient, and Taylor number.